Solution: The GCF of 150 and 35 is 5
Methods
How to find the GCF of 150 and 35 using Prime Factorization
One way to find the GCF of 150 and 35 is to compare the prime factorization of each number. To find the prime factorization, you can follow the instructions for each number here:
What are the Factors of 150?
What are the Factors of 35?
Here is the prime factorization of 150:
2
1
×
3
1
×
5
2
2^1 × 3^1 × 5^2
2 1 × 3 1 × 5 2
And this is the prime factorization of 35:
5
1
×
7
1
5^1 × 7^1
5 1 × 7 1
When you compare the prime factorization of these two numbers, you can see that there are matching prime factors. You can now find the Greatest Common Factor of 150 and 35 by multiplying all the matching prime factors to get a GCF of 150 and 35 as 25:
Thus, the GCF of 150 and 35 is: 25
How to Find the GCF of 150 and 35 by Listing All Common Factors
The first step to this method of finding the Greatest Common Factor of 150 and 35 is to find and list all the factors of each number. Again, you can see how this is done by looking at the “Factors of” articles that are linked to above.
Let’s take a look at the factors for each of these numbers, 150 and 35:
Factors of 150: 1, 2, 3, 5, 6, 10, 15, 25, 30, 50, 75, 150
Factors of 35: 1, 5, 7, 35
When you compare the two lists of factors, you can see that the common factor(s) are 1, 5. Since 5 is the largest of these common factors, the GCF of 150 and 35 would be 5.
Find the GCF of Other Number Pairs
Want more practice? Try some of these other GCF problems:
What is the GCF of 133 and 127?
What is the GCF of 7 and 141?
What is the GCF of 21 and 145?
What is the GCF of 137 and 51?
What is the GCF of 130 and 16?